Japheth and Lee have some money. If Japheth gives $314 to Lee, the ratio of their money will be 3 : 5. If Japheth gives $531 to Lee, the ratio of their money will be 1: 4. How much does Japheth have?
|
Case 1 |
Case 2 |
|
Japheth |
Lee |
Japheth |
Lee |
Before |
15 u + $314 |
25 u - $314 |
8 u + $531 |
32 u - $531 |
Change |
- $314 |
+ $314 |
- $531 |
+ $531 |
After
|
3x5 = 15 u |
5x5 = 25 u |
1x8 = 8 u |
4x8 = 32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Japheth has at first is the same in both cases.
15 u + 314 = 8 u + 531
15 u - 8 u = 531 - 314
7 u = 217
1 u = 217 ÷ 7 = 31
Amount that Japheth has
= 15 u + 314
= 15 x 31 + 314
= 465 + 314
= $779
Answer(s): $779